Finding The Probability Of Winning The Texas Lottery Video



Winning the Lottery


Finding the Probability of Winning the Texas Lottery – I show how to calculate the probability of you winning the Texas Lottery game “Texas Millions” if you buy one ticket.
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okay in this video I want to talk about the Texas Millions lottery that’s in a Texas and the way that you win the Texas Millions lottery is there’s basically a big container whatever of balls that are numbered 1 through 56 you pick 5 so 5 balls come out so maybe it’s 25 17 8:30 to 9:00 you have to pick those five balls the order that they come out doesn’t matter okay so you can pick the balls in any order and then you also have to pick there’s a different colored ball that you have to pick exactly correct as well and it’s labeled one through 46 so that one it could even be possible that one of the numbers would repeat itself okay with one of these new ones okay so we want to figure out the probability here that you would win the lottery if you buy exactly one lotto ticket in this case okay so really something like this we just want to turn it into a statement so what are we really calculating we’re calculating that we pick um all five of the original balls that come out and we pick the one correct the one will say the one special ball okay well these are independent events whether or not I cake the you know the five balls that came out of the one the one tub whether or not I pick those is going to happen if I pick those correctly it’s going to have no out no impact on whether or not I pick the correct one special ball so in this case okay these are going to be independent events so we have to calculate the probability of picking the five balls correctly and we’ll multiply that by the probability of us picking the one special ball correctly one special ball okay so in this case this is where our counting techniques come into play here okay so the probability of us getting the first five balls correctly okay well we only have one guess what we need to do though is count the total number of ways that those five balls can show up since we’re counting without replacement and order doesn’t matter this is where we use combinations so there was a total of 56 balls and we have to choose five of those okay so that’ll be the probability of us picking the five balls correctly and then we also have to pick this one special ball correctly and remember there there were only 46 choices okay since I only have one pick there’s just a one in 46 chance of me picking that one correctly all right so this is now the probability of us getting the of winning the Texas lotto okay so now we need to compute these things 56 juice pop 5 and 1 over 46 and just as a reminder the 1 over 56 choose 5 that’s 56 factorial divided by 51 factorial times 5 factorial so you may want to look at my combinations video if you haven’t seen this just yet but I calculated um I actually just multiplied these two numbers together I forgot the exact number that I got for 56 factorial over 51 factorial times 5 factorial it was a pretty big number in the denominator but if you multiply this number by 46 you actually get the following number as the probability of you winning the lottery it says the probability of you winning the lottery is so let me give myself a little more space here let me let me erase this and put it right here just the probability of you winning the Texas Lottery is point 0 0 0 0 0 0 let’s see 3 6 9 ok we got 9 zeros 1 2 3 4 5 6 7 8 9 5 6 9 1 1 ok and again just as a reminder point 0 1 is a 1 percent probability that you win the Texas Lottery so that’s the probability of you winning the lottery and in exactly if you buy exactly one ticket here in Texas just for a little little reference the probability of you getting struck by lightning if you live in the USA seems to hover somewhere around point 0 0 0 0 3 2 all right so just to kind of compare the probability of you getting struck by lightning versus the probability of you becoming a millionaire because of your fortuitous guessing but as the the slick advertisements say right somebody’s got to win so but uh maybe buy a ticket or two just don’t turn your whole paycheck over all right I hope this makes some sense if you have any questions just send me an email.

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